1. Field of the Invention
This invention relates to an improvement in the temperature dependence of a silicon semiconductor diffused strain gage.
2. Description of the Prior Art
A conventional pressure sensor is shown in FIG. 1 wherein impurity atoms are diffused in a silicon substrate to form a strain gage. An n-type silicon (Si) substrate 1 and a p-type diffused resistance 2 is formed, for example, by diffusion or ion implantation. An insulation layer 3, made of SiO.sub.2, is formed over the diffused resistance layer, then contact holes 4a-4d and electrodes 5 are disposed in the insulation layer 3. A diaphragm 8 of about 20 to 50 .mu.m thickness is formed by etching a portion of the rear face of the silicon substrate 1.
The resistivity of such a diffused resistance (resistance value per unit cross sectional area and unit length) .rho. can generally be represented by the following equation (1): EQU .rho.=1/(e(u.sub.po .multidot.P+u.sub.no .multidot.n)) (1)
wherein e is the elementary electric charge; u.sub.po is the positve hole mobility (quantity indicating the velocity of positive holes upon applying unit voltage between electrodes); u.sub.no is the electron mobility (quantity indicating the velocity of electrons upon applying unit voltage between electrodes); P is the positive hole density; and n is the electron density.
Assuming that the diffused resistance 2 shown in FIG. 1 is formed with a kind of impurity atoms forming acceptors, which is uniformly distributed, equation (1) can be expressed by the following approximate formula (2): EQU .rho.=1/(e.multidot.u.sub.po .multidot.P) (2)
It can be seen from equation (2) that the value of resistivity .rho. is dependent on the positive hole mobility u.sub.po and the positive hole density P. That is, it can be considered that the temperature dependence of resistivity consists of temperature dependence of the positive hole mobility u.sub.po and the temperature dependence of positive hole density P.
It is known that positive hole density P takes substantially a constant value within a range of from -100.degree. C. to 200.degree. C., which is referred to as a saturation region, and is equal to the acceptor density in the portion of the diffused resistance layer 2. Accordingly, when the semiconductor strain gage is used within the temperature range as described above, the temperature dependence of the resistivity is determined by the temperature dependence of positive hole mobility u.sub.po.
It can be stated that a greater positive hole mobility u.sub.po means that the positive holes move through the diffused resistance 2 while undergoing no substantial scattering, whereas a smaller u.sub.po means that the positive holes are less movable in the direction of the electric field due to the substantial scattering.
The scattering mechanism hindering the movement of the positive holes can include
(1) scattering due to thermal vibration of the lattice atoms constituting crystals (the mobility is referred to as a lattice scattering mobility and represented by u.sub.L), and
(2) scattering due to ionized acceptor atoms (the mobility is referred to as an ionized impurity scattering mobility and is expressed by u.sub.I).
The positive hole mobility u.sub.po in the case where the scattering mechanisms are present together is represented as follows: EQU 1/u.sub.po =1/u.sub.L +1/u.sub.I ( 3)
That is, the temperature dependency of the positive hole mobility u.sub.po is dependent on the lattice scattering mobility u.sub.L and the ionized impurity scattering mobility u.sub.I. The temperature dependency of u.sub.L and u.sub.I can be represented by the following equations: EQU u.sub.L .alpha.(m*).sup.-2/5 .multidot.T.sup.-3/2 ( 4) EQU u.sub.I .alpha.(m*).sup.-1/2 .multidot.T.sup.3/2 /N.sub.I ( 5)
wherein m* is the effective mass of positive hole or electron; N.sub.I is the density of impurity doped in the diffused resistance (hereinafer referred to as the acceptor density); T is the absolute temperature (.degree.K.).
FIG. 2 is a view depicting the relationship between the positive hole mobility u.sub.po (cm.sup.2 /V.sec) and the temperature (.degree.K.) obtained by substituting equation (4) and equation (5) into equation (3). It shows the characteristic curve at each acceptor density N.sub.I (wherein N.sub.i =1.3.times.10.sup.18, 2.7.times.10.sup.18 cm.sup.-3) within the range of the absolute temperature T=100 to 600.degree. K.
FIG. 3 corresponds to the hatched area in FIG. 2 and shows the characteristic curve at each acceptor density N.sub.I (wherein N.sub.I = 10.sup.14, 10.sup.16, 10.sup.17, 10.sup.18, 10.sup.19 cm.sup.-3) within the range of absolute temperature T=223.degree.-473.degree. K.
Referring to the two curves in FIG. 2, the portion shown by the dotted chain, wherein positive hole mobility is increased along withe increase in temperature, is a region wherein u.sub.I represented by equation (5) is predominant. On the other hand, the portion represented by the solid line, wherein positive hole mobility is decreased along with increase in temperature, is a region wherein u.sub.L represented by equation (4) is predominant.
FIG. 3 is an enlarged view of a protion near room temperature (about 300.degree. K.) wherein u.sub.L is predominant and it can be seen from the drawing that although the effect of u.sub.I becomes significant as acceptor density N.sub.I is increased and positive hole mobility u.sub.po is lowered, it has less temperature dependence. That is, although resistivity .rho. shown by the equation (2) decreases, variation caused by the temperature change decreases.
FIG. 4 shows the relationship between temperature and the resistance normalized by the value at 25.degree. C. and the variation (%) while temperature is varied from 25.degree. C. to 125.degree. C. using a p-type diffused resistance of 3 .mu.m depth (sheet resistivity is 50, 100, 150, 200, 500 .OMEGA./.quadrature.) to an n-type Si substrate.
In the case of a bipolar IC (integrated circuit), the resistance value used is generally from 110 to 200 .OMEGA./.quadrature.. It can be seen from FIG. 4 that the temperature dependence of resistivity within this range is as high as about 0.2%/degree. By doping acceptor impurity N.sub.I in about 10.sup.19 cm.sup.-3, although temperature dependency is decreased, the resistivity .rho. is also lowered as shown in FIG. 3. That is, when calculating resistivity .rho. according to equation (2) assuming the positive hole density P=10.sup.19 cm.sup.-3, electric charge e=1.6.times.10.sup.-19 and the positive hole mobility u.sub.po =30 (at N.sub.I = 10.sup.19 cm.sup.-3 and 298.degree. K. (i.e. 25.degree. C.) in FIG. 3), .rho. is as small as EQU .rho.=1/(1.6.times.10.sup.19 .times.30.times.10.sup.19)=0.02 .OMEGA.cm.
It is difficult to apply such a low resistivity to diffused resistance since the length of the resistance should be increased or the width of the resistance should be decreased, for example.
In the conventional semiconductor strain gage, the problem of great temperature dependence of the resistivity (the temperature coefficient of resistivity) is overcome with a method of offsetting such a variation by using a differential system, such as a bridge circuit. However, if there is any unbalance between the resistances in the bridge circuit complete offset is impossible. Further, in addition to the above problem, such a resistance has a temperature coefficient of the piezoresistance coefficient, that is, the sensitivity as a strain gage drifts, depending on the temperature. Accordingly, complex temperature compensation circuits have been connected to the subsequent stages.
Thus, it can be definitely stated that the prior art devices have many deficiencies and disadvantages.